A contractor plans to install a slide for children under 5. The top of the slide is at a height of 1.5 m, and it is inclined at an angle of 30° to the ground. What should be the length of the slide?

Step 1: Identify the given information and the unknown

We are given the height of the slide, which forms the perpendicular side of a right-angled triangle. The angle of inclination with the ground is also provided. We need to find the length of the slide, which represents the hypotenuse of this right-angled triangle.

Step 2: Choose the appropriate trigonometric ratio

In a right-angled triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle (perpendicular) to the length of the hypotenuse. Since we know the perpendicular and the angle, and we need to find the hypotenuse, the sine ratio is the most suitable choice.

Step 3: Substitute the values and solve for the length of the slide

We substitute the given values into the sine ratio. The value of $\sin 30^\circ$ is $1/2$. By cross-multiplication, we can solve for $AC$, which is the length of the slide.

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